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When does Raoult's law become a special case of Henry's law?

Last updated date: 19th Jul 2024
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Hint :Raoult's law is named after François-Marie Raoult, a French chemist who discovered during an experiment that when liquids were combined in a solution, the solution's vapour pressure reduced at the same time. Raoult's law, also known as the law of thermodynamics, was developed in the year 1887.

Complete Step By Step Answer:
The partial vapour pressure of a solvent in a solution (or mixture) is equal to or equivalent to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution, according to Raoult's law.
Raoult's law equation is written mathematically as
 $ {p_{solution}} = {X_{solvent}}{p^o}_{solvent} $
 $ {p_{solution}} $ = vapour pressure of the solution
 $ {X_{solvent}} $ = mole fraction of the solvent
 $ {p^o}_{solvent} $ = vapour pressure of the pure solvent

When the temperature is held constant, Henry's law states that the volume of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid. Henry's law constant is the proportionality constant for this relationship. Henry's rule has the following mathematical formula:
 $ P = {K_H}C $
‘P’ denotes the partial pressure of the gas in the atmosphere above the liquid.
‘C’ denotes the concentration of the dissolved gas.
‘ $ {K_H} $ ’ is the Henry’s law constant of the gas.

When $ {K_H} $ equals $ {p_1}^o $ in Henry's law, Raoult's law becomes a special case of Henry's law.
Liquids evaporate at a certain temperature. The pressure exerted by the liquid vapour on the liquid phase at equilibrium is referred to as vapour pressure.
According to Raoult’s law:
 $ p{\text{ }} = {\text{ }}{p^o}x $
p is the partial pressure
x is the mole fraction
 $ {\text{ }}{p^o} $ is the vapour pressure of the pure component.
According to Henry’s law:
p = $ {K_H} $ x
p is the partial pressure, and x is the mole fraction.
 $ {K_H} $ is the proportionality constant (Henry’s constant)
By comparing the two equations, we can see that the volatile component's or gas's partial pressure is directly proportional to its mole fraction in solution. As a result, since $ {\text{ }}{p^o} = {K_H} $ , Raoult's law is a special case of Henry's law.
Only for 'ideal' mixtures (mixtures obeying Raoult's law over the full spectrum of composition), which do not exist, is Henry's constant roughly equal to the vapour pressure. Still, in this case, closely related compounds like benzene and toluene may form a near-ideal combination.
In opposing composition ranges, Raoult's and Henry's laws are followed.
As a result, Raoult's law is a subset of Henry's law.

Note :
At room temperature and pressure, elements that live as gases are found on the right side of the periodic table as either monatomic gases (the noble gases) or diatomic molecules (some halogens, N₂, O₂). Gases expand naturally to fill the vessels in which they are stored, resulting in a volume equalisation.